🔗 Tsiolkovsky Rocket Equation

🔗 Spaceflight 🔗 Physics 🔗 Rocketry

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity can thereby move due to the conservation of momentum.

${\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}=I_{\text{sp}}g_{0}\ln {\frac {m_{0}}{m_{f}}}}$

where:

${\displaystyle \Delta v\ }$ is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).

${\displaystyle m_{0}}$ is the initial total mass, including propellant, also known as wet mass.

${\displaystyle m_{f}}$ is the final total mass without propellant, also known as dry mass.

${\displaystyle v_{\text{e}}=I_{\text{sp}}g_{0}}$ is the effective exhaust velocity, where:

${\displaystyle I_{\text{sp}}}$ is the specific impulse in dimension of time.

${\displaystyle g_{0}}$ is standard gravity.

${\displaystyle \ln }$ is the natural logarithm function.